Abstract
This paper presents a new formula for calculating the hardness of metallic crystals, resulted from the research on the critical grain size with stable dislocations. The formula is H = 6 kG/[π(1 − ν)e η], where H is the hardness, k the coefficient, G the shear modulus, ν the Poisson’s ratio, η a function of the radius of an atom (r) and the electron density at the atom interface (n). The formula will not only be used to testify the critical grain size with stable dislocations, but also play an important role in the understanding of mechanical properties of nanocrystalline metals.
Similar content being viewed by others
References
Cheng K J and Cheng S Y 1996 Prog. Nat. Sci. 6 12
Cheng K J and Cheng S Y 2001 Prog. Nat. Sci. 11 701
El-Sherik A M, Erb U, Palumbo G and Aust K T 1992 Scripta Metall. et Mater. 27 1185
El-Sherik A M, Shirokoff J and Erb U 2005 J. Alloys Compd. 389 140
Gryaznov V G, Kaprelov A M and Romanov A E 1989 Scripta Metall. 23 1443
Gryaznov V G, Polonsky I A, Romanov A E and Trusov L I 1991 Phys. Rev. B44 42
Ke M, Hackney S A, Milligan W W and Aifantis E C 1995 Nanostruct. Mater. 5 689
Li S C 2004 Prog. Nat. Sci. 14 113
Misra A, Verdier M, Lu Y C, Kung H, Mitchell T E, Nastasi M and Embury J D 1998 Scripta Mater. 39 555
Nieh T G and Wadsworth J 1991 Scripta Metall. et Mater. 25 955
Ren F Z, Zhou G S, Zheng M S, Zhao W Z and Gu H C 2004 Rare Metal Mat. Eng. 3 933 (in Chinese)
Siegel R W and Fougere G E 1995 Nanostruct. Mater. 6 205
Schuh C A, Nieh T G and Yamasaki T 2002 Scripta Mater. 46 735
Wang N, Wang Z R, Aust K T and Erb U 1995 Acta Metall. Mater. 43 519
Yu Y N 2000 Metallography principles (Beijing: Metallurgical Industry Press) Ch. 6 (in Chinese)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, W., Ren, F., Su, J. et al. Hardness of metallic crystals. Bull Mater Sci 34, 943–946 (2011). https://doi.org/10.1007/s12034-011-0219-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12034-011-0219-9